Stochastic scheduling has received much attention from both industry and academia. Existing works usually focus on random job processing times. However, the uncertainty existing in job release times may largely impact the performance as well. This work investigates a stochastic parallel machine scheduling problem, where job release times and processing times are uncertain. The problem consists of a two-stage decision-making process: (i) assigning jobs to machines on the first stage before the realisation of uncertain parameters (job release times and processing times) and (ii) scheduling jobs on the second stage given the job-to-machine assignment and the realisation of uncertain parameters. The objective is to minimise the total cost, including the setup cost on machines (induced by job-to-machine assignment) and the expected penalty cost of jobs' earliness and tardiness. A two-stage stochastic program is proposed, and the sample average approximation (SAA) method is applied. A scenario-reduction-based decomposition approach is further developed to improve the computational efficiency. Numerical results show that the scenario-reduction-based decomposition approach performs better than the SAA, in terms of solution quality and computation time.

随机调度受到了工业界和学术界的广泛关注。现有工作通常侧重于随机作业处理时间。但是，职位发布时间存在的不确定性也可能在很大程度上影响绩效。这项工作研究了一个随机并行机调度问题，其中作业发布时间和处理时间是不确定的。该问题由两阶段的决策过程组成：（i）在实现不确定参数（作业发布时间和处理时间）之前将作业分配给第一阶段的机器；（ii）在给定的第二阶段调度作业作业到机器的分配和不确定参数的实现。目标是最小化总成本，包括机器上的设置成本（由作业到机器的分配引起）和作业提前和迟到的预期惩罚成本。提出了一个两阶段随机程序，并应用了样本平均近似（SAA）方法。进一步开发了基于场景缩减的分解方法以提高计算效率。数值结果表明，基于场景简化的分解方法在解决方案质量和计算时间方面的性能优于 SAA。